Re: [eigen] inverse unit test

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

2010/6/10 Gael Guennebaud <gael.guennebaud@xxxxxxxxx>:
>
>
> 2010/6/10 Adolfo Rodríguez Tsouroukdissian
> <adolfo.rodriguez@xxxxxxxxxxxxxxxx>
>>
>>
>> On Thu, Jun 10, 2010 at 9:42 AM, Manuel Yguel <manuel.yguel@xxxxxxxxx>
>> wrote:
>>>
>>> I hit the same problem several times and the implementation of
>>> isMuchSmallerThan for float is:
>>>
>>> inline bool ei_isMuchSmallerThan(float a, float b, float prec =
>>> NumTraits<float>::dummy_precision())
>>> {
>>>  return ei_abs(a) <= ei_abs(b) * prec;
>>> }
>>>
>>> if b is zero, then whatever prec is, it will failed if a is not zero,
>>> so I do agree with Hauke that his implementation is needed.
>>> So in fact in my own code I finally used the function he proposed.
>>>
>>>
>>
>> Here's my 2 cents.
>>
>> The VectorBase and MatrixBase classes apart from implementing the
>> isApprox(...) method, implement the very convenient:
>>
>> bool isZero       (const T & precision = Util::epsilon<T>()) const
>> bool isNegligible (const T & other, const T &  precision =
>> Util::epsilon<T>()) const
>> bool isNegligible (const Derived & other, const T &  precision =
>> Util::epsilon<T>()) const
>>
>
> Where did you find the isNegligible functions? Anyway isNegligible would be
> an alias for isMuchSmallerThan.
>
> Regarding isZero, yes we added it for "convenience" but I think it is more
> difficult to use than isMuchSmallerThan unless you are in the specific case
> where your values are in the order of 1. Otherwise you have to compute
> yourself what is the ideal epsilon matching your case, and this is more
> difficult than simply specifying a reference value of your non zeros because
> this "ideal" epsilon depends on the scalar type. In other word, with
> isMuchSmallerThan you only have to bother about the typical range of your
> non zeros, while with a isZero function you also have to take care at the
> scalar type.
>
> Now I acknowledge that in many cases, 1 is a good reference value, and so
> yes why not adding such a isZero for scalars as well nut with a big warning
> because it has to be used with care. Let's see what Benoit thinks about
> that.
>
> gael

Just confirming that I agree with everything Gael said here :)

I had forgotten about isZero and I think it's a bad idea that we have
it, I'd advocate removing it, forcing people to use
isMuchSmallerThan(ref). This forces people to think about which
reference to use to compare.

Benoit

>
>>
>> For convenience and parallelism with the Vector and Matrix types classes,
>> it would be nice to have the isZero(...) and isNegligible(...) functions
>> defined for Scalar types as well. Granted, isZero(val, prec) ==
>> isMuchSmallerThan(val,1.0, prec), but the former is less verbose and much
>> easier to understand.
>>
>> Adolfo
>>
>>> - cheers,
>>>
>>> Manu
>>>
>>>
>>
>>
>>
>> --
>> Adolfo Rodríguez Tsouroukdissian, Ph. D.
>>
>> Robotics engineer
>> PAL ROBOTICS S.L
>> http://www.pal-robotics.com
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>> Fax.+34.93.209.11.09
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>